With the win, the African champions move to the fifth spot on the log with 22 points from 10 games thus far.
The opening eight minutes saw the hosts controlling the proceedings, not allowing Sundowns to play, but they failed to trouble goalkeeper Wayne Sandilands.
However, the first opportunity came when Hlompho Kekana produced his trademark thunderbolt from a distance, but was collected by keeper Patrick Tignyemb in the 13th minute.
As Pitso Mosimane’s men dominated the proceedings, they were awarded a set piece not far from the box with 11 minutes to go in the half. Kekana again forced Tignyemb to produce a superb save to parry it from danger.
With one minute to the interval, Siwelele wasted two chances to grab the lead as their first attempt was cleared on the line by Thapelo Morena and Sandilands was alert to stop the second.
Sundowns continued to trouble Siwelele in the second half, but Tignyemb denied them and Ricardo Nascimento came close to breaking the deadlock when he failed to direct a cross from the left flank in to the net.
Siwelele caught their visitors on a counter and Deon Hotto’s well placed shot to the far corner produced a wonderful save from Sandilands in the 75th minute.
With 12 minutes remaining, substitute Zwane scored for the visitors when he showed composure after receiving a sweet pass from another substitute, Leonardo Castro, in the penalty area.
Percy Tau nearly bagged another when he showed his magic in the 83rd minute, beating Wandisile Letlabika and Tignyemb in the box, only to be denied by the woodwork.
The last four minutes saw Zwane providing his defensive magic when he cleared Celtic’s corner with the ball looking like it crossed the line.
Lehlohonolo Seema’s men tried to get a point, but they failed to break the solid Sundowns defence as they move to number 13 on the log table.